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In predictable mobile networks, network nodes move in a predictable way and therefore have dynamically changing but predictable connectivity. We have developed a model that formalizes predictable dynamic topologies as sequences of static snapshots. We use this model to design and evaluate a predictable mobile-routing protocol based on link-state routing, whose performance is superior to its static and ad hoc counterparts. Our routing protocol accounts for occurrences of additional, unpredictable changes, as well as their interaction with predictable changes. We evaluate our protocol using simulations based on randomly generated topologies and spacecraft-network scenarios. In both cases, we show that our protocol outperforms traditional routing protocols and is well suited for routing in next-generation space networks.